Zeros of a Quadratic Polynomial Video Explanation Question Find the zeros of the quadratic polynomial \[ f(x) = x^2 – 2x – 8 \] and verify the relationship between the zeros and their coefficients. Solution Step 1: Find the Zeros of the Polynomial Given: \[ f(x) = x^2 – 2x – 8 \] Factorising the […]

Condition on r in Euclid’s Division Lemma Video Explanation Watch the video below for a clear explanation: Solution Question: Euclid’s division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq + r where r must satisfy: Euclid’s Division Lemma Condition According to

Find the HCF and LCM of 12, 21 and 15 Video Explanation Watch the video below for a clear explanation: Solution Question: The HCF and LCM of 12, 21 and 15 respectively are: (a) 3, 140    (b) 12, 420    (c) 3, 420    (d) 420, 3 Step 1: Prime Factorisation 12 = 22

Product of a Non-Zero Rational Number and an Irrational Number Video Explanation Watch the video below for a clear explanation: Solution Question: The product of a non-zero rational number and an irrational number is: (a) always irrational    (b) always rational    (c) rational or irrational    (d) one Key Concept A rational number can

Largest Number Which Divides 70 and 125 Leaving Given Remainders Video Explanation Watch the video below for a clear explanation: Solution Question: The largest number which divides 70 and 125, leaving remainders 5 and 8 respectively, is: (a) 13    (b) 65    (c) 875    (d) 1750 Step 1: Subtract the Remainders 70 −

Find the HCF of a = x³y² and b = xy³ Video Explanation Watch the video below for a clear explanation: Solution Question: If two positive integers a and b are written as a = x3 y2 b = x y3 where x and y are prime numbers, then find HCF(a, b). (a) xy   

Nature of p12 − p22 When p1 and p2 Are Odd Prime Numbers Video Explanation Watch the video below for a clear explanation: Solution Question: If p1 and p2 are two odd prime numbers such that p1 > p2, then p12 − p22 is: (a) an even number    (b) an odd number    (c)

Number of Decimal Places in the Decimal Expansion of 33/(22 × 5) Video Explanation Watch the video below for a clear explanation: Solution Question: The decimal expansion of the rational number 33 / (22 × 5) will terminate after: (a) one decimal place    (b) two decimal places    (c) three decimal places    (d)

Condition for n² − 1 to Be Divisible by 8 Video Explanation Watch the video below for a clear explanation: Solution Question: n² − 1 is divisible by 8, if n is: (a) an integer    (b) a natural number    (c) an odd integer    (d) an even integer Step 1: Factorise the Expression

General Form of an Odd Integer Video Explanation Watch the video below for a clear explanation: Solution Question: For some integer q, every odd integer is of the form: (a) q    (b) q + 1    (c) 2q    (d) 2q + 1 Key Concept An odd integer is an integer that is not